49th IEEE Conference on Decision and Control (CDC) 2010
DOI: 10.1109/cdc.2010.5717190
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Communication, convergence, and stochastic stability in self-assembly

Abstract: Existing work on programmable self-assembly has focused on deterministic performance guarantees-stability of desirable states. In particular, for any acyclic target graph a binary rule set can be synthesized such that the target graph is the uniquely stable assembly. If the number of agents is finite, communication and consensus algorithms are necessary for the dynamic process induced by the rule set to converge to a state with a maximum number of target assemblies. We suggest a self-assembly problem constrain… Show more

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Cited by 13 publications
(10 citation statements)
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“…However, our convergence rate bounds may be conservative in this regard. Furthermore, as we will show in Section IV, a significantly smaller value of β may often be chosen in order to further speed convergence while still retaining the asymptotic properties guaranteed in (9).…”
Section: B Semi-anonymous Potential Gamesmentioning
confidence: 99%
“…However, our convergence rate bounds may be conservative in this regard. Furthermore, as we will show in Section IV, a significantly smaller value of β may often be chosen in order to further speed convergence while still retaining the asymptotic properties guaranteed in (9).…”
Section: B Semi-anonymous Potential Gamesmentioning
confidence: 99%
“…In [3] the authors presented a nearly identical algorithm as a standalone system without the notation of graph grammars. The algorithm is a recursion.…”
Section: A Serial Algorithmmentioning
confidence: 99%
“…In this framework, assemblies are network topologies. The precursor paper [3] used weighted graphs to confer geometric orientations on the edges, but we omit these details here in the interest of simplicity.…”
Section: A Graph Grammarsmentioning
confidence: 99%
“…Two formal rule-synthesis algorithms, Singleton and Linchpin, are introduced in the same work. In [4], weighted graphs are considered in a case study to encode the geometric orientations of the edges. Stochastic SA of simulated underwater robots in 3D using a rule-based approach has been studied in [5].…”
Section: Introductionmentioning
confidence: 99%